Time: 20 minutes. This quiz is open book, open notes.
"A bag contains a bean that is known either to be white or black. A white bean is added to the bag, the bag is shaken, and one bean is taken out at random. It is white. What, now, is the chance that the bean left in the bag is white?"
Suppose you do some further research and ascertain that, at the beginning of the problem (before adding the white bean), the probability that the bag contains a black bean is 2/3.
1. This problem concerns a sequence of events: place a bean into a bag; after adding the white bean, draw one bean, then observe the remaining bean. Write down all possible sequences and determine their probabilities.
2. Model the sequences of outcomes using a single box model.
3. Answer the question: "What, now, is the chance that the bean left in the bag is white?"
4. Write down an Excel expression that will be equal to -1 10% of the time (at random) and equal to 1 90% of the time.
Scoring: The passing score is 90.
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